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arXiv 0812.4504hep-thastro-phgr-qc
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全息、UV/IR关系、因果熵界与暗能量

Holography, UV/IR Relation, Causal Entropy Bound and Dark Energy

Rong-Gen Cai, Bin Hu, Yi Zhang

备注：
Latex, 15 pages with 3 eps files. Submitted to Comm. Theor. Phys; v2: typos corrected and a few references added
发表信息：
Commun.Theor.Phys.51:954-960,2009
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摘要：

在一个给定的空间区域中，对总能量的约束是由全息术给出的，即刚好适合该区域的黑洞的质量，这导致了UV/IR关系：该区域中的最大能量密度与$M_p^2/L^2$成比例，其中$M_p$是普朗克质量，$L$是所考虑的该区域的空间尺度。假设宇宙中最大的黑洞是通过宇宙中扰动的引力坍缩形成的，那么扰动的“金斯”尺度给出了因果联系尺度$R_{\rm CC}$。对于引力微扰，$R^{-2}_{\rm CC}={\rm Max}(\dot H+2H^2, -\dot H)$表示平坦宇宙。在真空能量密度分别作为独立的守恒能量分量和有效的宇宙动力学宇宙学常数的情况下，通过选择因果联系标度作为UV/IR关系中的IR截止，研究了相应真空能量密度的宇宙动力学.事实证明，只有选择$R_{\rm CC}^{-2}= \dot H +2H^2$的情况下，才能与当前的宇宙学观测相一致，当真空密度出现作为一个独立的守恒能量分量时。在这种情况下，文献中称该模型为全息Ricci标量暗能量模型。

英文摘要：

The constraint on the total energy in a given spatial region is given from holography by the mass of a black hole which just fits in that region, which leads to an UV/IR relation: the maximal energy density in that region is proportional to $M_p^2/L^2$, where $M_p$ is the Planck mass and $L$ is the spatial scale of that region under consideration. Assuming the maximal black hole in the universe is formed through gravitational collapse of perturbations in the universe, then the "Jeans" scale of the perturbations gives a causal connection scale $R_{\rm CC}$. For gravitational perturbations, $R^{-2}_{\rm CC}={\rm Max}(\dot H+2H^2, -\dot H)$ for a flat universe. We study the cosmological dynamics of the corresponding vacuum energy density by choosing the causal connection scale as the IR cutoff in the UV/IR relation, in the cases of the vacuum energy density as an independently conserved energy component and an effective dynamical cosmological constant, respectively. It turns out that only the case with the choice $R_{\rm CC}^{-2}= \dot H +2H^2$, could be consistent with the current cosmological observations when the vacuum density appears as an independently conserved energy component. In this case, the model is called holographic Ricci scalar dark energy model in the literature.

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